The Liverpool manager, Brendan Rodgers, believes his side still retain a glimmer of hope as they seek a first title since 1990, despite appearing to blow their chances in the final straight.

Manchester City require only a draw at home to West Ham on Sunday to wrap up a second championship in three seasons given that their goal difference is vastly superior to their title rivals'. Liverpool go into their meeting with Newcastle at Anfield trailing City by two points and Rodgers knows that only a West Ham win would give his side an opportunity of overtaking them.

However, with their former striker Andy Carroll – deemed surplus to requirements at Anfield by Rodgers – leading the attack for Sam Allardyce's side, the Northern Irishman has clearly not given up.

"It's certainly not over. We know it is a tough game for us. For City, West Ham have some talented players and, if they can go to Tottenham and win 3-0, then they can certainly go to City and win," Rodgers said.

"We will fight to the very end. If we win the game and don't win the title, then to finish second to the richest team in sport is a huge compliment to what we are doing.

"They've got Big Andy up front and they can cause real problems. The expectancy is City will win but it won't be easy for them. West Ham know they have the players who can cause problems."

Having won a club record 11 games in succession, Liverpool led the table by five points going into the showdown with Chelsea at Anfield on 27 April but Steven Gerrard's uncharacteristic mistake allowed José Mourinho's side to win 2-0 and hand the initiative back to City. Crystal Palace's late comeback from 3-0 down at Selhurst Park on Monday further diminished their chances of securing a first Premier League title but Rodgers expects his players to learn from that disappointment.

"I've watched the Palace match three times and I'm still in shock," he said.

"But I'd like to congratulate my players. We have had a remarkable season and put Liverpool on the world map again.

"This is only the beginning. I think we will improve dramatically again next season – the young players will be better for what they have experienced."

Rodgers also confirmed he has an agreement in principle over a new contract, which he hopes will be signed when the season concludes. With Champions League qualification secured for the first time since the 2009-10 season, several new arrivals are expected this summer to bolster his squad. However, Rodgers was steadfastly noncommittal when asked whether Southampton's England winger Adam Lallana is one of his primary targets.

"I'm sure you can respect that I would never, ever mention about a player at another club," he said. "It is purely speculation. Adam is a terrific young talent but for us there is always speculation about top young players."